(1. 中南大学地球科学与信息物理学院，长沙 410083；
2. 东华理工大学核资源与环境教育部重点实验室，南昌 330013)
摘 要: 利用最小梯度支撑稳定因子进行2.5D井地电位聚焦反演。通过对边界近似处理、结合基于图论理论的矩阵重排与填入元分析方法，实现一种快速的正演稀疏矩阵直接分解方法，提高了正演计算效率。为了突出对陡变异常体边界的识别能力，引入最小梯度支撑稳定因子(MGS)，采用重加权共轭梯度(RRCG)方法进行反演目标函数求解。结果表明：MGS具有良好的聚焦特征，RRCG反演迭代过程稳定、收敛速度快。对“L-curve”选择正则化因子的算法进行改进，避免了传统采用最大曲率计算时需要对离散数据求导引起的误差，同时该算法对于出现多个拐点的“L-curve”也可正确选择正则化因子。
关键字: 井地电位法；重加权共轭梯度法； L-curve；最小梯度支撑稳定因子；LDLT分解算法
（1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. Key Laboratory of Nuclear Resources and Environment, Ministry of Education,
East China Institute of Technology, Nanchang 330013, China）
Abstract:The 2.5D focusing inversion for borehole-to-ground electric potential was implemented using minimum gradient support function. The boundary approximation, matrix rearrangement and fill-in element analysis algorithm based on graph theory were adopted to complete the fast algorithm of direct decomposition method for sparse matrix, the computational efficiency was improved. In order to improve the inversion ability to discriminate boundary of abnormal bodies, the minimum gradient support stability factor (MGS) was adopted. On the other hand, re-weighted regularized conjugate gradient (RRCG) inversion method was applied to solve inverse function. The results show that the stability factor is good at invert sharp boundary of underground bodies, RRCG method is stable and fast. For the rapid selection of the most suitable regularization factor, the revised “L-curve” algorithm was studied. New method based on the simply principle of distance from point to line, the error caused by the derivation of discrete data was avoided when the regularization factor was calculated using the maximum curvature method, moreover, for multiple inflection point of the “L-curve”, it also can select the best regularization factor.
Key words: borehole-surfaceelectrical method; re-weighted regularized conjugate gradient; L-curve; minimum gradient support function; LDLT factorization
